Growing Trees and Amoebas' Replications
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912332896010240 |
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| author | Gurvich, Vladimir Krnc, Matjaž Vyalyi, Mikhail |
| author_facet | Gurvich, Vladimir Krnc, Matjaž Vyalyi, Mikhail |
| contents | An amoeba is a tree together with instructions how to iteratively grow trees by adding paths of a fixed length $\ell$. This paper analyses such a growth process. An amoeba is mortal if all versions of the process are finite, and it is immortal if they are all infinite. We obtain some necessary and some sufficient conditions for mortality. In particular, for growing caterpillars in the case $\ell=1$ we characterize mortal amoebas. We discuss variations of the mortality concept, conjecture that some of them are equivalent, and support this conjecture for $\ell\in\{1,2\}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07484 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Growing Trees and Amoebas' Replications Gurvich, Vladimir Krnc, Matjaž Vyalyi, Mikhail Combinatorics Discrete Mathematics 05C75, 05C05 An amoeba is a tree together with instructions how to iteratively grow trees by adding paths of a fixed length $\ell$. This paper analyses such a growth process. An amoeba is mortal if all versions of the process are finite, and it is immortal if they are all infinite. We obtain some necessary and some sufficient conditions for mortality. In particular, for growing caterpillars in the case $\ell=1$ we characterize mortal amoebas. We discuss variations of the mortality concept, conjecture that some of them are equivalent, and support this conjecture for $\ell\in\{1,2\}$. |
| title | Growing Trees and Amoebas' Replications |
| topic | Combinatorics Discrete Mathematics 05C75, 05C05 |
| url | https://arxiv.org/abs/2401.07484 |